According to Avogadro's hypothesis, two samples of gas of equal volume, at the same temperature and pressure, contain the same number of molecules. But is there any proof of this? We can't possibly count the total molecules in two different gases of equal volumes at equal temperature and pressure. Then how did we arrive at this hypothesis? If not experemental, is there any Mathematical proof of this statement? Even the exact number of atoms or molecules in 1 mole of any substance is known and is termed as Avogadro's Number. How was is found? How did we know the exact number of molecules present in 1 mole of a substance? Please provide the derivation if any.

According to Avogadro's hypothesis, two samples of gas of equal volume

1.	According to Avogadro's hypothesis, two samples of gas of equal volume, at the same temperature and pressure, contain the same number of molecules. But is there any proof of this? We can't possibly count the total molecules in two different gases of equal volumes at equal temperature and pressure. Then how did we arrive at this hypothesis? If not experemental, is there any Mathematical proof of this statement? Even the exact number of atoms or molecules in 1 mole of any substance is known and is termed as Avogadro's Number. How was is found? How did we know the exact number of molecules present in 1 mole of a substance? Please provide the derivation if any.
Answer» According to Avogadro's hypothesis, two samples of gas of equal volume, at the same temperature and pressure, contain the same number of molecules. But is there any proof of this? We can't possibly count the total molecules in two different gases of equal volumes at equal temperature and pressure. Then how did we arrive at this hypothesis? If not experemental, is there any Mathematical proof of this statement? Even the exact number of atoms or molecules in 1 mole of any substance is known and is termed as Avogadro's Number. How was is found? How did we know the exact number of molecules present in 1 mole of a substance? Please provide the derivation if any.